Aptitude - Problems on H.C.F and L.C.M - Discussion

Why 1 is added? please explain.

If two bells toll after every 3 secs and 4 secs respectively and if they commence tolling at the same time.

Then the first bell tolls after every 3, 6, 9, 12 secs...
The second bell tolls after every 4, 8, 12, ....
So they toll together again after 12 secs, which is the LCM

Henceforth they toll after every 12 seconds, i.e whenever the time is a common multiple of both 3 and 4.

Since the bells start tolling together, the first toll also needs to be counted. Therefore we need to add 1.

Super explanation sundar.

So We need to count that first commence according to your answer.

But according to the question we need to find the time after first tolling together na ?

WoW...super explanation .thank you:)

Commense is nothing but start tolling. here six bells are there and toll together at intervals 2,4,6,8,10,12

first bell tolls at every :2secs,4secs,6sec......120sec....

second bell tolls at every :4secs,8secs,12secs.....120secs.....

third bell tolls together at every:6sec,12sec,18sec..120sec...

fourth bell tolls together at every:8sec,16sec,24sec...120sec..

fifth bell tolls together at every:10sec,20sec,30sec ,....120sec...

sixth ell tolls together at every:12sec,24sec,36sec....120sec...

NOW OBSERVE ALL TOLLS the common sec in *All* bell tolls is 120sec

thats why we need to find l.c.m in shortcut
come to question:
1 toll altogether takes time=120sec
? tolls altogether takes time=1800sec(30min*60sec)

The number of tolls are 1800*1/120 = 15 tolls(times)


But in question:
Six bells commence tolling together(first toll) and also toll at intervals of 2, 4, 6, 8 10 and 12 beginning itself started from tollinf so we should consider that toll also.

Hence answer is 15 Tolls + First Toll == 16 dat's it.

Hope you understand.

Excellent sravan now I understand everything in the question n wt you said. Its really very helpful to me. , AND YOUR EXPLANATION IS VERY VERY CLEAR.

THAN YOU VERY MUCH sravan!

Why do you divide 30 by 2?

Forget about 30/2, look at the answer given by Sravan. 1800/120=15

Thanks Sravan.

Excellent sravan.